链环连通分支数与Lefschetz数

Component Number of Links and Lefschetz Numbers

设f:(D2 ,A)→ (D2 ,A)是二维圆盘的一个保定向自同胚 ,其中A是D2 内部的有限点集 .从D2的恒同映射到f的任何同痕限制在A上是一个辫 ,对应的闭辫是R3 中的链环 .在本文中 。

Lef f:(D\+2,A)→(D\+2,A) be an orientation preserving self\|homeomorphism,where A is a set consisting of finitely many points in the interior of D \+2.The restriction of any isotopy form the identity map of D 2 to f is a braid,the closed braid of which is a link in R 3. We shall in this paper present some formulae showing the relation between the component number of such a link and the Lefschetz numbers of f and its iterates.